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We present a detailed theoretical study of the thermoelectric properties of the bismuth oxychalcogenides Bi _2 ChO _2 (Ch = S, Se, Te). The electrical transport is modelled using semi-classical Boltzmann transport theory with electronic structures from hybrid density-functional theory, including an approximate model for the electron lifetimes. The lattice thermal conductivity is calculated using first-principles phonon calculations with an explicit treatment of anharmonicity, yielding microscopic insight into how partial replacement of the chalcogen in the bismuth chalcogenides impacts the phonon transport. We find very good agreement between the predicted transport properties and a favourable cancellation of errors that allows for near-quantitative predictions of the thermoelectric figure of merit ZT . Our calculations suggest recent experiments on n-doped Bi _2 SeO _2 have achieved close to the largest ZT possible in bulk materials, whereas the largest reported ZT for Bi _2 TeO _2 could be improved sixfold by optimising the carrier concentration. We also predict that much larger ZT > 2.5, competitive with the benchmark thermoelectric SnSe, could be obtained for Bi _2 SO _2 and Bi _2 SeO _2 with heavy p-type doping. This study demonstrates the predictive power of this modelling approach for studying thermoelectrics and highlights several avenues for improving the performance of the Bi _2 ChO _2 .